Quantum collision theory in flat bands

Manuel Valiente Cifuentes, Nikolaj Thomas Zinner

Research output: Contribution to journalArticlepeer-review

7 Citations (Scopus)


We consider quantum scattering of particles in media exhibiting strong dispersion degeneracy. In particular, we study flat-banded lattices and linearly dispersed energy bands. The former constitute a prime example of single-particle frustration while the latter show degeneracy at the few- and many-particle level. We investigate both impurity and two-body scattering and show that, quite generally, scattering does not occur, which we relate to the fact that transition matrices vanish on the energy shell. We prove that scattering is instead replaced by projections onto band-projected eigenstates of the interaction potential. We then use the general results to obtain localized flat band states that are eigenstates of impurity potentials with vanishing eigenvalues in one-dimensional flat bands and study the particular case of a sawtooth lattice. We also uncover the relation between certain solutions of one-dimensional systems that have been categorized as 'strange', and the scattering states in linearly dispersed continuum systems.

Original languageEnglish
Article number064004
JournalJournal of Physics B: Atomic, Molecular and Optical Physics
Issue number6
Publication statusPublished - 7 Mar 2017


  • few-body physics
  • flat bands
  • scattering theory

ASJC Scopus subject areas

  • Atomic and Molecular Physics, and Optics
  • Condensed Matter Physics


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